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How to solve an algebra problem by substitution?

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Quick Answer

In algebra, the method of substitution is used to simplify problems by reducing the number of variables or quantities. The specific details of the solution depend on the original problem.

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How to solve an algebra problem by substitution?
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Full Answer

A classic case of algebraic substitution is an expression and the value of a variable, for example, x + 5 with x = 10. To evaluate the first expression, substitute the given value of x to find (10) + 5 = 15. Because x and 10 are the same value, the x in the initial expression can be replaced with 10 and a value can be found.

Another example in which substitution can be used to solve an algebraic expression is in the case of a system of linear equations. Consider the following; x + y = 10 and x - y = 6. Substitution can be used to solve the system by first solving the second equation for x as follows, x = 6 + y, and then substituting this expression for x into the first equation as follows, (6 + y) + y = 10, so 2y = 4, and y = 2. Use substitution once more to replace either equation's y variable with the value 2 to find x + (2) = 10, so x = 8.

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